A 20 kg shell is fired and reaches the top of its trajectory, P, where its velocity is purely horizontal. It explodes into three fragments A (5 kg), B (9 kg), and C (6 kg). Immediately after the explosion, fragment A is observed to have a vertical velocity and reaches a height of 500 m above P. What was the speed of fragment A immediately after the explosion? (Use g = 9.81 m/s^2)
Explanation
This question uses the principle of conservation of mechanical energy for a projectile. The initial kinetic energy of the fragment immediately after the explosion is converted into gravitational potential energy as it rises to its peak height.
Other questions
For a system of particles, the generalized Newton's second law is expressed as ΣF = ma. What does the term 'a' represent in this equation?
A system consists of three particles in a two-dimensional plane. Particle 1 has mass 2m and velocity 2v in the positive y-direction. Particle 2 has mass m and is stationary. Particle 3 has mass 4m and velocity v in the positive x-direction. What is the velocity vector of the center of mass for this system?
The total kinetic energy of a mass system can be expressed as the sum of two components. According to Article 4/3, what are these two components?
Three small spheres with masses of 0.3 kg, 0.8 kg, and 0.5 kg are connected by cords and are supported on a smooth horizontal surface. If a horizontal force of 6.4 N is applied to one of the cords, what is the acceleration of the mass center of the spheres?
How is the linear momentum G of a system of particles with constant mass defined?
What is the relationship between the resultant external force ΣF acting on a mass system and the system's linear momentum G?
When is the total linear momentum of a mass system conserved?
What does the equation ΣMO = H_O_dot represent for a system of particles, where O is a fixed point?
Under what condition is the angular momentum of a system about its mass center G conserved?
What is the primary characteristic of steady mass flow as defined in Article 4/6?
For a system undergoing steady mass flow, the force-momentum equation is ΣF = m_dot * Δv. What does the term ΣF represent?
Fresh water (density 1000 kg/m^3) issues from a nozzle at a velocity of 30 m/s and at a rate of 0.05 m^3/s. The stream is split into two equal streams by a fixed vane, where each stream is deflected 60 degrees from the original direction. What is the magnitude of the force F required to hold the vane in place?
A jet of air issues from a nozzle with a velocity of 300 ft/sec at a rate of 6.50 ft^3/sec. The specific weight of the air is 0.0753 lb/ft^3. The jet is deflected by a fixed right-angle vane. Calculate the force F required to hold the vane in place, assuming the speed of the air is unchanged.
A jet aircraft with a mass of 4.6 Mg has a drag of 32 kN while flying at a constant speed of 1000 km/h. The engine consumes air at a rate of 106 kg/s and fuel at 4 kg/s. The exhaust has a rearward velocity of 680 m/s relative to the nozzle. What is the maximum angle of elevation at which the jet can fly at this constant speed?
For a body whose mass is changing, the equation of motion is given as ΣF = mv_dot + m_dot*u. What does this equation represent?
In the context of rocket propulsion as described in Article 4/7, what does the thrust T of the rocket depend on?
A rocket at the instant of vertical launch expels exhaust at a rate of 220 kg/s with an exhaust velocity of 820 m/s. If the initial vertical acceleration of the rocket is 6.80 m/s^2, what is the total mass of the rocket and fuel at launch? (Use g = 9.81 m/s^2)
In the alternative approach to solving variable-mass problems described in Article 4/7, what is the key requirement for choosing the system?
What is the primary reason that the equation of motion ΣF = ma does not apply to systems with changing mass?
A chain of length L and mass per unit length ρ is lifted vertically from a platform with a constant velocity v. Using the variable-mass approach on the moving portion of the chain (of length x), what is the required lifting force P as a function of x?
During the lifting of the chain in Sample Problem 4/10, energy is lost. What is the source of this energy loss?
A rocket of initial total mass m0 is fired vertically. The fuel burns at a constant rate m_dot, and the exhaust has a constant relative velocity u. If the residual mass of the rocket is mb, what is the maximum velocity reached by the rocket, neglecting air resistance and gravity variation?
What is the key difference in the analysis of a flexible rope being lifted from a coil versus an open-link chain, as discussed in Sample Problem 4/11?
A fire tug discharges salt water (density 1030 kg/m^3) with a nozzle velocity of 40 m/s at a rate of 0.080 m^3/s. The water stream is directed 30 degrees above the horizontal. To maintain a fixed position, what propeller thrust T must the tug develop?
The work-energy equation for a system of particles, T1 + V1 + U'_1-2 = T2 + V2, relates the initial and final states of energy. What does the term U'_1-2 represent?
A 7-Mg jet airplane is launched from an aircraft carrier with a constant acceleration over a distance of 100 m along an angled takeoff ramp (15 degrees above horizontal). The carrier moves at a steady 16 m/s. If an absolute aircraft speed of 90 m/s is desired, what is the net force F supplied by the catapult and the aircraft engines?
Three freight cars are rolling along a horizontal track. Car A has weight 130,000 lb and velocity 2.0 mi/hr. Car B has weight 100,000 lb and velocity 1.0 mi/hr. Car C has weight 150,000 lb and velocity 1.5 mi/hr. All velocities are in the same direction. The cars collide and become coupled together. What is the common velocity of the system after impact?
A jet-engine noise suppressor consists of a movable duct that deflects the engine blast directly upward. During a ground test, the engine sucks in air at 43 kg/s and burns fuel at 0.8 kg/s. The exhaust velocity is 720 m/s. What is the tension T in the cable that secures the duct?
A flexible, nonextensible rope of mass ρ per unit length and length equal to 1/4 of the circumference of a fixed drum of radius r is released from rest in a horizontal position. When the rope comes to rest, what is the loss of energy ΔQ of the system?
A carriage of mass 2m is free to roll and carries two spheres, each of mass m, on rods of length l. The system is released from rest with the rods in the vertical position (angle theta = 0). What is the velocity of the carriage, vx, when the rods reach the horizontal position (angle theta = 180 degrees)?
Why is the linear momentum of the system NOT conserved in problem 4/94, where a bullet embeds itself in a pendulum?
What is the primary distinction between the equations of motion for a system with steady mass flow (Article 4/6) and a system with variable mass (Article 4/7)?
A 2-oz bullet is fired horizontally with a velocity of 1000 ft/sec into a 3-lb pendulum initially at rest. The bullet embeds itself in the pendulum bar. Treating the pendulum bob as a particle and neglecting the rod's mass, what is the resulting angular velocity of the pendulum immediately after impact if the pendulum length to the bob is 10 inches?
A rotating frame consists of four 3-kg balls rigidly mounted to a shaft. The balls are located at a radius of 0.5 m from the vertical axis of rotation. The system is initially rotating freely at 20 rad/s clockwise. A constant torque of 30 N-m is applied to the shaft in the counter-clockwise direction. How long does it take to reverse the direction of rotation and reach an angular velocity of 20 rad/s counter-clockwise?
What does the term 'impulse' represent in the context of kinetics of systems of particles?
In Sample Problem 4/2, which determines the motion of three balls welded to a rigid frame, why is the angular acceleration of the frame independent of the distance 'b' where the force F is applied?
For the exploding shell in Sample Problem 4/4, why is the linear momentum of the system (the collection of three fragments) conserved during the explosion?
A 32.2-lb carriage moves horizontally at 4 ft/sec. It carries two rotating assemblies. Each of the four balls on the assemblies weighs 3.22 lb. What is the magnitude G of the linear momentum of the entire system?
In the system from Sample Problem 4/5, two balls rotate counter-clockwise at 80 rev/min at a radius of 18 inches, and two rotate clockwise at 100 rev/min at a radius of 12 inches. What is the contribution to the total kinetic energy from the rotational motion of the particles relative to the carriage?
Why does the term Σf, the vector sum of all internal forces, equal zero in the derivation of the equation of motion for a system of particles?
A jet of fluid with mass density ρ and cross-sectional area A issues from a nozzle with velocity v and impinges on a smooth, inclined trough. The trough is held in position by a resultant force F normal to its surface. If some fluid is diverted into stream 1 and the rest into stream 2, and the speed v remains the same for both streams, what is the required force F?
A 90-degree vane moves to the left at a constant velocity of 10 m/s. It is struck by a stream of fresh water (density 1000 kg/m^3) from a 25-mm-diameter nozzle, issuing to the right with a velocity of 20 m/s. What is the horizontal force Fx required to support the vane's motion?
A helicopter with mass m hovers by imparting a downward velocity v to a column of air of radius r, where the pressure is atmospheric. If the air has density ρ, what is the power P required of the engine, neglecting rotational energy and temperature changes?
A space shuttle is in an equatorial circular orbit of 240-km altitude, moving from west to east. What is the magnitude of the velocity it appears to have to an observer B fixed on the equator as the shuttle passes directly overhead? Use earth radius R = 6378 km and g = 9.81 m/s^2.
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Two small spheres, each of mass m, are rigidly connected by a rod and slide down a smooth circular guide of radius r in a vertical plane. They are released from rest with the rod in a horizontal position. What is their common speed v as they reach the position where the rod is vertical?
In the context of the work-energy relation for a system of particles (Article 4/3), when does no net work get done by internal interacting forces?
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